UPSC NDA Math Model Paper 1

Since m + n and m - n are roots of the quadratic equation, by factor theorem, (x-(m-n)) and (x-(m+n)) are the factors of the quadratic equation.
Therefore, the quadratic equation is given by:
(x−(m−n))(x−(m+n)) =x2−x(m+n)−x(m−n)+(m +n)(m−n) =x2−x(m+n+m−n)+(m2−n2) =x2−2mx+(m2−n2)
Therefore, the required equation is x2−2mx+(m2−n2)
Note that as all the options have leading coefficient 1 we can directly calculate the equation by simply multiplying the factors.